I'm reading that the ultimate goal in training our Chows for obedience is to just rely on the voice command without any treats. Walter doesn't have any problems with treat training and with hand signals but when I remove either of the two, it seems that he doesn't obey. I'm not doing it abruptly as recommended but I don't see any improvement. He still depends on the liver treat before he gets excited and does all the "moves" I taught him. Is this really how Chows behave during training or am I missing something here?

Chows are mostly going to do what you want because it benefits them. If they figure out that there is no reward at the end, then they probably will ignore you. That doesn't mean that it has to be a food reward. During training, its just the easiest way to get to the end result. Once Walter has demonstrated he will do something repeatedly, you can switch to a non-food reward. You will want to congratulate him with enthusiastic praise, or a really good ear scratch, belly rub, whatever. Tossing him a really nice slipper may even work for him. You really won't know until you try.

Now at some point he will do the basics just because he knows what to do, he will likely sit just because you gave him the hand signal, or will wait at the door because you told him to, but in his mind he still has that reward system in the back of his head.

A chow will almost always need to believe that he is doing something for a specific (positive) reason. He can actually analyze the situation and make his decision based on what he expects to get out of it.

So, I wouldn't abandon rewards completely (again, they don't have to be food based after a certain success level). It's not bad to have him thinking that sometimes it happens, sometimes it doesn't, so this might be the time it does.

When I train him, I try to alternate (in no repetitive interval) between giving him food and just simply praising him by petting his head or his chin. I do this every time I train him but when I try to do a test on him without pulling out food treats, I don't get positive responses from him. He does like petting him but I'm not sure if that's enough for him to consider as a "reward" for something positive that he does. So when you say switch to a non-food reward, are you saying to completely abandon food and do something else that he likes or do I need to alternate between food and non-food?

I would alternate in a non-random manner. You really can't abandon food rewards. His motivation is going to come from the possibility of a food reward in most cases. That is also how you build the pack order. He needs to know that you are the alpha because you control the resources. If he doesn't like the rain, you are the one that lets him inside and provides a warm, dry space. When he is hungry, you provide the food (otherwise he goes and hunts). Be the one that provides a quick scratch to his itch....etc. When that is established, he will willingly do what you ask him once he is taught what that is. Food is just the easiest and quickest way to get to that point.